Looks like a broken solder joint to me or the motherboard has sockets for the 2 battery pins and the one pictured is just bent.
It definitely needs to make contact all the time.

That kind of battery holder is held on by 3 pins.
The 3 board mounted parts serve as a 3-pin socket to plug the holder into.

The corner you are lifting up still has the pin, it's just been bent up under the holder.

Only two pins (+) and (-) are needed but I don't know if the disconnected one is one of them.
If there is no electrical connection to the 3rd (disconnected) pin on the mobo side there isn't any reason to do anything.
Same same if there are two pins to ground and the bent one is one of them. One ground is enough.
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You were right. The '+' pin was bent 😀
If I need to replace the battery, I will solder a new holder, but I only have 2 pins holders. You seem to say that the two '-' pins are both conected to ground, so it shouldn't be an issue?

If you can straighten the pin without breaking it then you won't need a new holder.
Mini pliers might get the job done without even removing it.

I can't tell where anything is connected from the photo.
Can't even tell if solder is needed. It might be a press-fit.

You have + and - and 3 pins.
It could be (not connected), +, - or +, +, - or +, -, -
You will have to look and see.

The two - and one + is most likely I think.
If that's the case and the bent one is the + then yes you need to fix it.
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